On the fully nonlinear Alt-Phillips equation

Abstract

For a parameter $\gamma \in (1,2)$, we study the fully nonlinear version of the Alt-Phillips equation, $F(D^{2}u)=u^{\gamma -1}$, for $u\ge 0.$ We establish the optimal regularity of the solution, as well as the $C^1$ regularity of the regular part of the free boundary.

20 pages; Typos corrected; New references included; Accepted by IMRN